hw06 - aries and Gauss-Seidel method for the same boundary...

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ENGR 8102: C OMPUTATIONAL E NGINEERING Problem Set 6 (due on Wednesday in my mailbox by 4pm, 11/10) Questions: 1. (4 pts.) Compute the L 1 , L 2 and L norms of the following vectors and periodic functions: (a) u = [ - 1 , 1 , 100 ] (b) v = [ 100 , - 100 , 100 ] (c) f ( θ ) = 1 (See footnote 1 ) (d) g ( θ ) = sin ( θ ) 2. (7 pts.) Write down the four coupled linear equations for the following system. Then rewrite them in matrix form ( Ax = b ), where x is a vector of temperature variables, b is vector of scalars, and A is a matrix of scalars. Find the values of T 11 , T 12 , T 21 and T 22 by solving this system ( x = A - 1 b ). T T T 1,1 2,2 T 2,1 1,2 10 15 20 25 30 25 25 20 3. (7 pts.) Modify the code jacobi_flow.m given in class, to feature a 20x20 grid (including bound-
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Unformatted text preview: aries) and Gauss-Seidel method, for the same boundary conditions. Plot the temperature distribution and isothermal lines (run enough iterations so that there is no visible error). Include a hard copy of your code and the graphs along with your solution. Submit a soft copy of your code as an attachment to [email protected] . 1 Here are the definitions of L 1 and L ∞ norms for 2 π periodic functions: k f ( θ ) k L 1 = 1 2 π Z 2 π | f ( θ ) | d θ , k f ( θ ) k L 2 = s 1 2 π Z 2 π [ f ( θ )] 2 d θ , k f ( θ ) k L ∞ = max < θ < 2 π | f ( θ ) | . 1...
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